Question
Two different dice are thrown together. Find the probability that the numbers obtained have
(i) Even sum, and
(ii) Even product.
(i) Even sum, and
(ii) Even product.
✓
Answer
The outcomes when two dices are thrown together
$\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \$2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \$3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \$4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \$5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \$6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
There are 36 total outcomes
(i) When sum of numbers is even
Let $\text {B}$ be the event of getting even sum.
$\left\{\begin{array}{l}(1,1),(1,3),(1,5) \$2,2),(2,4),(2,6) \$3,1),(3,3),(3,5) \$4,2),(4,4),(4,6) \$5,1),(5,3),(5,5) \$6,2),(6,4),(6,6)\end{array}\right\}$
There are 18 favourable outcomes.
Probability for even sum outcomes
$P(A)=\frac{18}{36}=\frac{1}{2}$
(ii) Even product outcome
Let $\text {B}$ be the event of getting even product.
$\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \$2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \$3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \$4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \$5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \$6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
There are 36 total outcomes
(i) When sum of numbers is even
Let $\text {B}$ be the event of getting even sum.
$\left\{\begin{array}{l}(1,1),(1,3),(1,5) \$2,2),(2,4),(2,6) \$3,1),(3,3),(3,5) \$4,2),(4,4),(4,6) \$5,1),(5,3),(5,5) \$6,2),(6,4),(6,6)\end{array}\right\}$
There are 18 favourable outcomes.
Probability for even sum outcomes
$P(A)=\frac{18}{36}=\frac{1}{2}$
(ii) Even product outcome
Let $\text {B}$ be the event of getting even product.
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